Interpolants for Runge-Kutta formulas

ABSTRACT

A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is presented. As illustrations, this approach is used to develop interpolants for three explicit RK formulas, including those employed in the well-known subroutines RKF45 and DVERK. A typical result is that no extra function evaluations are required to obtain an interpolant with O(h5) local truncation error for the fifth-order RK formula used in RKF45; two extra function evaluations per step are required to obtain an interpolant with O(h6) local truncation error for this RK formula.

REFERENCES

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INDEX TERMS

Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.1 Interpolation
          Subjects: Interpolation formulas
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems; One-step (single step) methods; Error analysis

General Terms:
Algorithms, Theory